Pre-Tango structures and uniruled varieties

Yoshifumi Takeda. "Pre-Tango structures and uniruled varieties." Colloquium Mathematicae 108.2 (2007): 193-216. <http://eudml.org/doc/283846>.

@article{YoshifumiTakeda2007,
abstract = { The pre-Tango structure is an ample invertible sheaf of locally exact differentials on a variety of positive characteristic. It is well known that pre-Tango structures on curves often induce pathological uniruled surfaces. We show that almost all pre-Tango structures on varieties induce higher-dimensional pathological uniruled varieties, and that each of these uniruled varieties also has a pre-Tango structure. For this purpose, we first consider the p-closed rational vector field induced by a pre-Tango structure, and the smoothness of the fibration induced by the p-closed rational vector field. Moreover, we give two examples: of a 3-dimensional variety of general type whose automorphism group scheme is not reduced, and of a non-uniruled variety which has a pre-Tango structure inducing a higher-dimensional pathological uniruled variety. },
author = {Yoshifumi Takeda},
journal = {Colloquium Mathematicae},
keywords = {Tango structure; pre-Tango structure; uniruled variety; -closed rational vector field},
language = {eng},
number = {2},
pages = {193-216},
title = {Pre-Tango structures and uniruled varieties},
url = {http://eudml.org/doc/283846},
volume = {108},
year = {2007},
}

TY - JOUR
AU - Yoshifumi Takeda
TI - Pre-Tango structures and uniruled varieties
JO - Colloquium Mathematicae
PY - 2007
VL - 108
IS - 2
SP - 193
EP - 216
AB - The pre-Tango structure is an ample invertible sheaf of locally exact differentials on a variety of positive characteristic. It is well known that pre-Tango structures on curves often induce pathological uniruled surfaces. We show that almost all pre-Tango structures on varieties induce higher-dimensional pathological uniruled varieties, and that each of these uniruled varieties also has a pre-Tango structure. For this purpose, we first consider the p-closed rational vector field induced by a pre-Tango structure, and the smoothness of the fibration induced by the p-closed rational vector field. Moreover, we give two examples: of a 3-dimensional variety of general type whose automorphism group scheme is not reduced, and of a non-uniruled variety which has a pre-Tango structure inducing a higher-dimensional pathological uniruled variety.
LA - eng
KW - Tango structure; pre-Tango structure; uniruled variety; -closed rational vector field
UR - http://eudml.org/doc/283846
ER -